CN110835782A - Cylindrical single crystal orientation butt joint method - Google Patents
Cylindrical single crystal orientation butt joint method Download PDFInfo
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Abstract
The invention relates to a cylindrical single crystal orientation butt joint method, which comprises the steps of obtaining Laue photos of a single crystal A sample and a single crystal B sample through a single crystal diffractometer, calibrating the Laue photos, respectively obtaining conversion matrixes of a crystallography coordinate system and a sample appearance coordinate system of the two single crystals, respectively calculating a crystal orientation deviation angle α and a crystal orientation azimuth angle β of the same non-axial crystal orientation of the two single crystals through the conversion matrixes, obtaining projection positions of the crystal orientation of the two single crystals on the side surface of the sample, enabling the crystal orientation projection positions of the obtained single crystal A and the obtained crystal orientation projection positions of the single crystal B to be coincident, and achieving butt joint of the single crystal A and the single crystal B.
Description
Technical Field
The invention relates to a single crystal orientation technology, in particular to a cylindrical single crystal orientation butt joint method.
Background
Two methods for determining the orientation of single crystals by X-ray polycrystal diffractometers exist at present.
The first is X-ray theta scan rotation ([1]]Application of novel XRD single crystal orientation device for Guoshenqi, Lifei and Zhushifu]Laboratory science 2011,14(6):92-96 [2 ]]Comparison of two methods for determining crystal face drift angle of refractory single crystal [ J]Physical and chemical inspection-physical inventory, 2016,52(1):17-20.), provided that the crystal system and lattice constant of the material are known, as shown in fig. 1, the diffraction angle theta of the target crystal face (HKL) is calculated according to the bragg diffraction law, then the included angle between the incident ray and the detector is fixed to be (pi-2 theta), and the incident ray, the diffracted ray and the sample macroscopic surface method are adoptedThe lines are coplanar (the plane is denoted as S), then the sample is rotated around the normal of the sample surface (the rotation speed is large enough to ensure that the sample can rotate one circle in each step of the theta scanning), the theta scanning is carried out simultaneously, the (HKL) crystal plane passes through the maximum diffraction intensity position twice (namely the position of the normal of the crystal plane parallel to the plane S), and a pair of diffraction peaks symmetrical about theta appear on the diffraction pattern shown in FIG. 2, and the positions are respectively denoted as theta1And theta2And half of the difference between the two is the deviation angle phi of the (HKL) crystal plane and the macroscopic surface of the sample. The method cannot directly determine the spatial orientation of the target crystal face, and needs to perform secondary measurement: reading out theta from diffraction spectrum obtained by X-ray theta rotation scanning1(or theta)2) Then still maintaining the probe 2 theta0At a fixed position of theta1(or theta)2) And (3) nearby scanning, rotating the sample at a low speed, and manually stopping when the maximum value of diffraction intensity is observed, wherein the target crystal face is perpendicular to a plane S formed by incident rays and diffraction rays, so that the spatial orientation of the target crystal face is determined.
The second method is the X-ray rocking curve method ([1] guo zhe, li fei, zhuyihu. XRD single crystal orientation new device application [ J ]. laboratory science, 2011,14(6):92-96.) which, like the first method, requires both rotation of the sample and theta scanning, except that rotation and scanning are not performed simultaneously. Specifically, the method comprises the steps of firstly placing a sample on a sample table, then carrying out theta scanning to determine a backswing curve every time the sample rotates 5 degrees around the surface normal direction until the sample rotates one circle. Next, a scatter diagram as shown in fig. 3 is drawn with the peak-to-peak position of each of the rocking curves as the abscissa and the number of rotations (or rotation angle) as the ordinate. In the figure, the maximum and minimum values of the abscissa are the deviation angle of the target crystal direction, and the ordinate corresponding to the maximum value of the abscissa is the coplanar position of the target crystal direction with the incident ray and the diffraction ray. The method has the advantage that the off-angle and the spatial orientation of the crystal plane can be determined simultaneously. The method has the disadvantages of too long measuring time and too low efficiency, and 72 backswing curves need to be measured.
The common disadvantage of the above two methods is that: (1) the deviation angle of each crystal orientation needs to be measured independently, which wastes time and labor; (2) whether the sample is single crystal or polycrystalline is judged by the number of diffraction peaks, and misjudgment may occur.
In addition, Tangshi red proposes a method for determining the orientation of a copper single crystal by combining chemical etching, laser and X-ray (3) orientation method research of copper single crystal by Zhao Jun, Beijun, Xuzhu, J. artificial crystal bulletin, 2011,40(2): 329) 332.). The test principle is as follows: firstly, etching a copper crystal ingot by using a nitric acid solution for a period of time to enable the surface of the crystal ingot to have a reflecting surface with consistent orientation, then using a laser 1 to emit a horizontal laser to the copper crystal ingot 2, and simultaneously enabling the horizontal laser to pass through a small hole 4 on a baffle 3, wherein a projection light spot is left on the baffle after the laser is reflected by a crystal face, as shown in figure 4. Through the position and the angle of adjustment crystal, let the facula and the aperture coincidence of reflecting back, incident ray and reflection line coincidence this moment, the reflection of light face is perpendicular with the light path, grinds the crystal with thick metallographical sand paper along the light path vertical direction, can find out the reflection of light face. And finally, analyzing the small crystal faces obtained by grinding by using an X-ray diffractometer, and determining the crystal orientation index of the reflecting face. And determining the crystal orientation indexes of the three reflecting surfaces by using a similar method so as to obtain any required crystal plane orientation. The disadvantages are as follows: (1) the sample needs to be corroded and ground, and the integrity of the sample is damaged; (2) the process is complicated, and the laser irradiation sample and the X-ray diffraction need to be repeatedly used for many times; (3) the universality is not strong enough, and different corrosion reagents and corrosion time are needed for single crystals made of different materials.
In addition, Lixin proposed a method for directionally butting single crystals by using an X-ray single crystal diffractometer ([4] Lixin, Renwei. Mo-3Nb single crystal directional welding technology research [ J ] rare metal materials and engineering, 2015,44(1): 190-. The measurement process is as follows: marking on the joint surface of two single crystal rods, respectively obtaining two Laue pictures by using a single crystal X-ray diffractometer, then rotating one sample (fixing by incident X-rays), obtaining a new Laue picture, finishing measurement until the superposition degree of the Laue pictures of the two samples is optimal, and butting the two samples according to the position. The method has the following defects: (1) the single crystal orientation process is complicated, and diffraction is carried out after many times of single crystal rotation; (2) the determination of the optimal superposition position of the laue photo depends on human eyes, and the human error is large; (3) the axial crystal direction of the bar is selected as an orientation reference, but the azimuth angle of the axial crystal direction is unstable and is not suitable for serving as the orientation reference.
Disclosure of Invention
The invention aims to provide an efficient, intuitive, universal and semi-automatic cylindrical single crystal orientation butt joint method aiming at the defects of the prior art so as to realize lattice matching between single crystal rods or tubes of the same type.
The technical scheme of the invention is as follows: a cylindrical single crystal orientation butt joint method comprises the following steps:
obtaining a Laue photo of a single crystal A sample through a single crystal diffractometer, and calibrating the Laue photo to obtain a transformation matrix T of a crystallographic coordinate system of the single crystal A and an appearance coordinate system of the sampleA；
According to a transformation matrix TACalculating to obtain a non-axial crystal orientation of the single crystal A<HKL>α (g)1And β1Corner, wherein, α1β is the deviation angle (0-90 DEG) of the crystal orientation with respect to the axial direction of the single crystal rod1Azimuth angle (0-180 degree) of the crystal orientation on the cross section of the single crystal rod according to β1Obtaining the projection position of the crystal direction of the single crystal A on the side surface of the sample;
obtaining a Laue photo of a single crystal B sample through a single crystal diffractometer, and calibrating the Laue photo to obtain a transformation matrix T of a crystallographic coordinate system of the single crystal B and an appearance coordinate system of the sampleB；
According to a transformation matrix TBCalculating to obtain the same non-axial crystal orientation of the single crystal B<HKL>α (g)2And β2Corner, wherein, α2β is the deviation angle (0-90 DEG) of the crystal orientation with respect to the axial direction of the single crystal rod2Azimuth angle (0-180 degree) of the crystal orientation on the cross section of the single crystal rod according to β2Obtaining the projection position of the crystal direction of the single crystal B on the side surface of the sample;
if | α1-α2If the value of | is within the acceptable range, the crystal orientation projection positions of the obtained single crystal A and the single crystal B are overlapped, and the butt joint of the single crystal A and the single crystal B is realized.
Further, the method for orientation butting of cylindrical single crystals as described above, wherein the off-angle α of the crystal orientation with respect to the axial direction of the single crystal ingot and the azimuth angle β of the crystal orientation on the cross section of the single crystal ingot are calculated by:
transformation matrix of crystallography coordinate system and sample appearance coordinate system
Three row vectors forming the matrix are unit vectors and are coordinates of three independent crystal directions in a sample appearance coordinate system respectively;
the three basic vectors of the appearance coordinate system of the sample are x, y and z, the three basic vectors of the crystallography coordinate system are a, b and c (respectively taking [100], [010] and [001]), and the relationship between the three basic vectors is as follows:
then, the corresponding direction vector of the crystal orientation [ HKL ] is denoted as n,
n＝(Ha1+Kb1+Lc1Ha2+Kb2+Lc2Ha3+Kb3+Lc3)
then, the calculation formulas for α and β are as follows:
wherein the vector npRepresenting the projection of the vector n in the plane oxy,
np＝(Ha1+Kb1+Lc1Ha2+Kb2+Lc20)。
further, the α and β values are relative to the current X-ray incidence position, if the sample is rotated, the α and β values need to be converted, and assuming that the sample is rotated clockwise or counterclockwise ± γ degrees (positive clockwise and negative counterclockwise) relative to the initial position, the formula for converting α and β is as follows:
α′＝α
where INT represents a gaussian integer function.
Further, the method for directionally butting cylindrical single crystals as described above, wherein the projection position of the crystal orientation of the single crystal a on the side surface of the sample is (β)1+180 deg. and the projection position of the crystal orientation of single crystal B on the sample side is β2The position of (a).
The invention has the following beneficial effects:
(1) the orientation representation of the crystal is more intuitive, wherein an α angle represents a crystal orientation deviation angle, a β angle represents a crystal orientation angle, and a β angle is used for determining the projection position of a reference crystal orientation on the side surface of the rod-shaped or tubular single crystal;
(2) the single crystal orientation process is semi-automatic, namely a single crystal diffractometer has a Laue photo calibration function, Excel can convert a calibration result into target parameters α and β through a predefined function, and an operator only needs to load and unload a sample and rotationally scribe, so that the working efficiency is greatly improved;
(3) the time is greatly shortened: the directional butt joint between two single crystal rods can be controlled within about 10 minutes, while the prior art generally needs more than one hour, and a rocking curve method even needs dozens of hours;
(4) nondestructive testing: the sample is not damaged in the orientation process;
(5) the shape of the diffraction spot is used as the basis for judging the single crystal and the polycrystal, so that misjudgment is not easy to occur.
Drawings
FIG. 1 is a schematic diagram of an X-ray theta scan rotation method;
FIG. 2 is a schematic diagram of a diffraction spectrum obtained by an X-ray theta rotation scanning method;
FIG. 3 is a diagram showing the results of the X-ray rocking curve method;
FIG. 4 is a schematic illustration of the determination of a reflective surface by laser reflection;
FIG. 5 is a schematic diagram of a single crystal diffractometer configuration;
FIG. 6 is a schematic illustration of the formation of a ribbon curve on a Laue photograph;
FIG. 7 is a schematic diagram of the relative positions of the appearance coordinate system and the crystallographic coordinate system of the sample;
FIG. 8 is a schematic view of a protractor and a disk for controlling the rotation angle of a columnar single crystal;
FIG. 9 is a schematic view of a directional scribe of a two-sided single crystal.
Detailed Description
The invention is described in detail below with reference to the figures and examples.
The present invention uses a single crystal X-ray diffractometer manufactured by german XRD Eigenmann GmbH, and the relative placement positions of the sample, the X-ray tube, and the sensor are shown in fig. 5. Prior to measuring the crystal orientation, the lattice type and lattice constant of the single crystal are known in advance, and the sample is required to be cylindrical (rod or tube). In addition, in order to eliminate the influence of the mechanical processing on the surface of the single crystal, the surface needs to be polished.
The basic principle of single crystal diffraction orientation is bragg's law, namely:
2dsin(θ)＝n·λ
the diffraction lines of the single crystal form Laue spots on the negative film or the fluorescent screen. The distribution of diffraction spots on laue photographs is regular, i.e. all spots are located on the quadratic curve. Specifically, the spots on the transmission laue picture are distributed on one ellipse, while the spots on the back-reflection laue picture are distributed on one hyperbola. In particular, all laue spots located on the same quadratic curve are produced by diffraction of the facets of the same band (these quadratic curves are therefore also referred to as band curves). FIG. 6 is a schematic illustration of the formation of a ribbon curve on a Laue photograph. If the sample is polycrystal, the Laue spot can not occur, so the method can not misjudge the monocrystal and the polycrystal.
The single crystal diffractometer of the method can realize the rapid automatic calibration of the laue photo, which is a well-known technology in the field, and the output result is a conversion matrix T of 3 multiplied by 3, namely:
the three row vectors forming the matrix are unit vectors and are coordinates of three independent crystal directions in a sample appearance coordinate system respectively. By converting the matrix T, the coordinates of the crystal orientation of any index in the sample appearance coordinate system can be obtained. How to calculate the spatial orientation of the crystal orientation [ HKL ] is described below.
The crystallographic coordinate system and the sample appearance coordinate system are shown in fig. 7. The three basic vectors of the appearance coordinate system of the sample are x, y and z, the three basic vectors of the crystallography coordinate system are a, b and c (respectively taking [100], [010] and [001]), and the relationship between the three basic vectors is as follows:
then, when the corresponding direction vector of the crystal orientation [ HKL ] is represented as n, the crystal orientation is expressed as n
n＝(Ha1+Kb1+Lc1Ha2+Kb2+Lc2Ha3+Kb3+Lc3)
In order to more intuitively represent the spatial orientation of the crystal, two angles α and β are introduced to represent the spatial orientation of the < HKL > crystal orientation relative to the sample appearance coordinate system, as shown in FIG. 7, wherein α represents the deviation angle (0-90) of the crystal orientation relative to the axial direction of the single crystal rod, and β represents the azimuth angle (0-180) of the crystal orientation on the cross section of the single crystal rod, similar to the definition of a three-dimensional spherical coordinate system, the calculation formulas of α and β are as follows:
wherein the vector npRepresenting the projection of vector n within plane oxy.
np＝(Ha1+Kb1+Lc1Ha2+Kb2+Lc20)
It should be noted that the α and β values are relative to the current X-ray incidence position, and if the sample undergoes rotation or translation, the α and β values need to be transformed to discuss the spatial orientation of the crystal under the same coordinate system the present invention considers only the rotation of the sample, assuming that the sample is rotated clockwise or counterclockwise by ± γ degrees (clockwise rotation takes positive values and counterclockwise rotation takes negative values) relative to the initial position, the transformation equations for α and β are as follows:
α′＝α
where INT represents a gaussian rounding function that is used to ensure β is between 0 and 180 degrees.
In general, each X-ray irradiation position may correspond to a laue photo and each laue photo may correspond to a transformation matrix, and after selecting the reference crystal orientation < HKL >, a pair of angles α and β may be obtained, and after understanding the specific meaning of angles α and β, the orientation butt joint of the single crystal may be performed.
Since the same preparation process of the same type of single crystal bars is the same, the deviation angle α of the crystal orientation < HKL > relative to the axial direction of a sample is the same or close, and the axial direction of a cylinder corresponds to the same crystal orientation (small deviation may exist), since the axial crystal orientations of the single crystal bars are matched, the oriented butt joint of the two side single crystal base materials can be realized only by superposing any non-axial crystal orientation.
The raw material used in the orientation experiment was a Mo alloy single crystal rod (Mo-3Nb) containing 3% Nb prepared by electron beam suspension zone melting furnace of the northwest nonferrous metals institute, the outer diameter was 25mm, and the axial crystal orientation was <111 >. in actual inspection, it was found that, with the <111> crystal orientation as the reference standard, the measured α angle was relatively stable (varying within 0-5 degrees) and the β angle fluctuation was relatively large (the variation may exceed 90 degrees), presumably because the axial direction of the single crystal rod was very close to the <111> crystal orientation, and the single crystal growth conditions and the external environment fluctuation easily caused the instability of the β angle (the actual off angle between the <111> crystal orientations at different positions was not large but enlarged during projection).
Firstly, marking the position of the crystal orientation on the single crystal: measuring arbitrary position of single crystal A<100>Orientation of crystal orientation to obtain α1And β1And then measuring an arbitrary position of the single crystal B<100>Orientation of crystal orientation to obtain α2And β2If α1And α2Very close values (α due to the same preparation process)1And α2Should be very close, as should the actual measurement), respectively at the a-terminal (β)1+180) degree position and β at the B-end2Degree position scribing (since the two ends of the AB are in face-to-face contact, the scribing position at one end requires a half turn). The thick lines in FIG. 9 represent A, B at both ends<HKL>The projection of the crystal orientation on the side surface of the single crystal round rod.
After the mark is made, the two-side single crystal is butted according to the mark, and the lattice matching of the two-side single crystal parent materials can be realized.
Examples
The raw material used in the directional experiment is a Mo alloy single crystal bar (Mo-3Nb) which is prepared by an electron beam suspension area smelting furnace of northwest nonferrous metals institute and contains 3% of Nb, the outer diameter is 25mm, and the axial crystal direction is <111 >. The complete process of single crystal orientation butt joint is specifically described as follows:
1) the calculation formula of α and β angles is input in advance in Excel, and [100] [010] [001] is preset in a single crystal diffractometer as a reference crystal orientation;
2) decontaminating and polishing the surface of the single crystal round rod;
3) as shown in fig. 8, the protractor is fixed on the single crystal a, the sample is placed and slightly leaned against the positioning probe, the sample is rotated until the pointer of the protractor coincides with 0 degree of the disc, the sample is fixed, and the sample stage is lifted to ensure that the X-ray is incident on the single crystal;
4) opening the X-ray high-voltage generator, closing the chamber, opening the X-ray baffle and starting single crystal diffraction;
5) automatically calibrating the Laue photo obtained by single crystal diffraction to obtain the corresponding transformation matrix TA；
6) Will convert the matrix TAInputting Excel to obtain [100] of single crystal A]α of crystal orientation1And β1Angle, rotate the sample so that the hands of the protractor are aligned with the discs (β)1+180) degree coincidence, and scribing at the 0 degree position of the sample;
7) closing the X-ray baffle, opening the chamber, taking out the single crystal A, taking down the protractor, fixing the single crystal A on the single crystal B, placing the single crystal B sample and slightly leaning on the positioning probe, rotating the sample until the pointer of the protractor is coincided with the 0 degree of the disc, and fixing the sample;
8) opening the X-ray high-voltage generator, closing the chamber, opening the X-ray baffle and starting single crystal diffraction;
9) automatically calibrating the Laue photo obtained by single crystal diffraction to obtain the corresponding transformation matrix TB；
10) Will convert the matrix TBInput Excel to obtain [100] of single crystal B]α of crystal orientation2And β2Angle, rotate the sample so that the index of the protractor is β of the disc2Overlapping, and scribing at the 0-degree position of the sample;
11) closing the X-ray baffle, opening the chamber, taking out the single crystal B, and taking down the protractor;
12) if | α1-α2If the value of | is within the acceptable range, the single crystals A and B are butted according to the mark, otherwise, the single crystals A and B are not butted, | α1-α2The acceptable range of | depends on the actual engineering requirements, and the higher the requirements on the material properties, the smaller the value should be. The range of this value in this embodiment may be within 5 degrees.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is intended to include such modifications and variations.
Claims (4)
1. A cylindrical single crystal orientation butt joint method is characterized in that:
obtaining a Laue photo of a single crystal A sample through a single crystal diffractometer, and calibrating the Laue photo to obtain a transformation matrix T of a crystallographic coordinate system of the single crystal A and an appearance coordinate system of the sampleA；
According to a transformation matrix TACalculating to obtain a non-axial crystal orientation of the single crystal A<HKL>α (g)1And β1Corner, wherein, α1The off-angle of the crystal orientation with respect to the axial direction of the single crystal rod, β1Azimuth angle of the crystal direction on the cross section of the single crystal rod according to β1Obtaining the projection position of the crystal direction of the single crystal A on the side surface of the sample;
obtaining a Laue photo of a single crystal B sample through a single crystal diffractometer, and calibrating the Laue photo to obtain a transformation matrix T of a crystallographic coordinate system of the single crystal B and an appearance coordinate system of the sampleB；
According to a transformation matrix TBCalculating to obtain the same non-axial crystal orientation of the single crystal B<HKL>α (g)2And β2Corner, wherein, α2The off-angle of the crystal orientation with respect to the axial direction of the single crystal rod, β2Azimuth angle of the crystal direction on the cross section of the single crystal rod according to β2Obtaining the projection position of the crystal direction of the single crystal B on the side surface of the sample;
if | α1-α2If the value of | is within the acceptable range, the crystal orientation projection positions of the obtained single crystal A and the single crystal B are overlapped, and the butt joint of the single crystal A and the single crystal B is realized.
2. The method of orientation butting of cylindrical single crystals according to claim 1, wherein the off-angle α of the crystal orientation with respect to the axial direction of the single crystal ingot and the azimuth angle β of the crystal orientation on the cross section of the single crystal ingot are calculated by:
transformation matrix of crystallography coordinate system and sample appearance coordinate system
Three row vectors forming the matrix are unit vectors and are coordinates of three independent crystal directions in a sample appearance coordinate system respectively;
the three basic vectors of the appearance coordinate system of the sample are x, y and z, the three basic vectors of the crystallography coordinate system are a, b and c (respectively taking [100], [010] and [001]), and the relationship between the three basic vectors is as follows:
then, the corresponding direction vector of the crystal orientation [ HKL ] is denoted as n,
n＝(Ha1+Kb1+Lc1Ha2+Kb2+Lc2Ha3+Kb3+Lc3)
then, the calculation formulas for α and β are as follows:
wherein the vector npRepresenting the projection of the vector n in the plane oxy,
np＝(Ha1+Kb1+Lc1Ha2+Kb2+Lc20)。
3. the cylindrical single crystal orientation butt joint method according to claim 2, wherein the α and β values are relative to the current X-ray incidence position, if the sample is rotated, the α and β values need to be converted, and assuming that the sample is rotated by + - γ degrees clockwise or counterclockwise relative to the initial position, the conversion formulas of α and β are as follows:
α′＝α
where INT represents a gaussian integer function.
4. The method of claim 1, wherein the projection position of the crystal orientation of the single crystal A on the sample side is (β)1+180 deg. and the projection position of the crystal orientation of single crystal B on the sample side is β2The position of (a).
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